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Bugs tunnels through the Himalayan mountains, followed by Daffy. After a failed attempt by Daffy to go swimming in a frozen pond, the two realize that they are not at their intended destination, Palm Springs.

Daffy, whilst underground, crashes into said creature's foot. The Abominable Snowman (whose name is Hugo, but that is not revealed in this short), grabs Daffy, names him George (a reference to Of Mice and Men, casting Hugo as Lennie Small to Daffy's George Milton), and gives him crippling hugs, believing Daffy is a rabbit, when actually Daffy just tied his sweater round his head for warmth, with the sleeves on top. Daffy reveals this by angrily yelling his head off, and Hugo proceeds to spank Daffy for his 'deception'. However, Daffy imparts to him where he can find a real rabbit i.e. Bugs. As Bugs starts experiencing Hugo's overbearing love, Daffy sneaks away. Hugo sits on Bugs, who sneaks out under the snow, carrying Daffy toward Hugo.

As Hugo doubts that Daffy is or isn't a rabbit, Daffy asks what a rabbit really looks like. Hugo responds that rabbits have long ears, making Bugs tie down his own ears and stick two of his fingers behind Daffy's head as rabbit ears. After Hugo painfully hugs the duck again but realizes that he has a bill and feathers, Daffy points out the tunneling Bugs to Hugo, who chases him underground. Eager to see the incident's conclusion, Daffy follows.

Later, in Palm Springs, a profusely sweating Hugo, and a disguised Bugs, discuss Hugo's failure to catch Bugs. Hugo believes that he will not be able to see the rabbit again, but Bugs encourages him that "if he loves you, he will come back." When Daffy emerges from the hole, Bugs puts fake rabbit ears on him, causing Hugo to recognize him as a rabbit again. While Daffy is cuddled for the last time, Hugo literally melts due to the intense heat of the environment. Bugs comments, "He really was a snowman!" and Daffy, soaked in water, replies, "Abominable, that is!"

The Abominable Snow Rabbit is included on the DVD collection Looney Tunes Golden Collection: Volume 5 as well as the VHS collections Looney Tunes After Dark and Bugs Bunny: Big Top Bunny. Most of the footage was also used in the compilation movie, Daffy Duck's Quackbusters for one part when Bugs and Daffy traveled to the Himalayas.